Apropos the OW lounge at LAX, there should be no problem accessing the OW lounge (for Sapphire or Emerald members), regardless of the class they are flying on MX. FYI I did so last weekend.

Am in MEX today for an onward flight to South America and was shocked to find that the Mexicana lounge (up on the 3rd floor with a out-of-order elevator) actually charges money for food & alcoholic drinks, even for Emerald passengers flying MX/J! Happily, the AA Admirals Club one floor down has no such issues!